Multiple Regression

Section: Multiple Regression Analysis Estimated study time: 60 minutes Content: Multiple regression is a cornerstone of quantitative finance and is tested extensively at CFA Level 2. The general multiple regression model takes the form: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + epsilon, where Y is the dependent variable, X1 through Xk are independent variables (predictors), b0 is the intercept, b1 through bk are slope coefficients, and epsilon is the error term. The ordinary least squares (OLS) estimator minimizes the sum of squared residuals. At Level 2, candidates must interpret regression output from a standard regression table, assess model quality, and identify violations of the classical linear regression model (CLRM) assumptions. The six CLRM assumptions are: (1) the relationship between the dependent and independent variables is linear in parameters; (2) the independent variables are not random and are not perfectly collinear with each other; (3) the expected value of the error term is zero — E(epsilon) = 0; (4) the variance of the error term is constant across all observations (homoskedasticity); (5) the error terms are uncorrelated with each other (no serial correlation); and (6) the error term is normally distributed. Violations of assumptions 4 and 5 — heteroskedasticity and serial correlation — are the most commonly tested at Level 2. These violations do not bias coefficient estimates but render standard errors (and therefore t-statistics and p-values) unreliable, leading to incorrect inference. Evaluating regression model fit involves several key statistics. The coefficient of determination (R-squared) measures the proportion of the dependent variable's variance explained by the regression: R-squared = SSR/SST = 1 - SSE/SST, where SST is total sum of squares, SSR is regression (explained)…